1
$\begingroup$

Consider a block matrix A

$$ A = \begin{pmatrix} A_{11} & A_{12}\\ A_{21} & A_{22} \end{pmatrix}_{2 \times 2} $$

such that its entries $A_{ij}$ are lower triangular matrices. What is the inverse of A? How and which norm can be used to show that the norm of matrix A is less than or equal one? And is there any relation between the eigenvalues of $A$ and the eigenvalues of lower triangular matrices $A_{ij}$?

$\endgroup$
0
$\begingroup$

if $A = \left [ \matrix{X & Y \\ W & Z} \right ]$, and we use the norm $\|M\| = \sqrt{\text{tr}(M^*M)}$, for all of them, then it is easy to see that $$\|A\|^2 = \|X\|^2 + \|Y\|^2 +\|W\|^2 +\|Z\|^2$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.